{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4a01e20c",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a89a2c2b",
   "metadata": {},
   "source": [
    "# 深度学习基础及数学原理\n",
    "深度学习并没有想象的那么难，甚至比有些传统的机器学习更简单。所用到的数学知识也不需要特别的高深，本章将会一边讲解深度学习中的基本理论，一边通过动手使用PyTorch实现一些简单的理论，本章内容很多，所以只做一个简短的介绍\n",
    "\n",
    "## 监督学习和无监督学习\n",
    "监督学习、无监督学习、半监督学习、强化学习是我们日常接触到的常见的四个机器学习方法：\n",
    "\n",
    "监督学习：通过已有的训练样本（即已知数据以及其对应的输出）去训练得到一个最优模型（这个模型属于某个函数的集合，最优则表示在某个评价准则下是最佳的），再利用这个模型将所有的输入映射为相应的输出。\n",
    "无监督学习：它与监督学习的不同之处，在于我们事先没有任何训练样本，而需要直接对数据进行建模。\n",
    "半监督学习 ：在训练阶段结合了大量未标记的数据和少量标签数据。与使用所有标签数据的模型相比，使用训练集的训练模型在训练时可以更为准确。\n",
    "强化学习：我们设定一个回报函数（reward function），通过这个函数来确认否越来越接近目标，类似我们训练宠物，如果做对了就给他奖励，做错了就给予惩罚，最后来达到我们的训练目的。\n",
    "这里我们只着重介绍监督学习，因为我们后面的绝大部们课程都是使用的监督学习的方法，在训练和验证时输入的数据既包含输入x，又包含x对应的输出y，即学习数据已经事先给出了正确答案。\n",
    "\n",
    "## 线性回归 （Linear Regreesion）\n",
    "线性回归是利用数理统计中回归分析，来确定两种或两种以上变量间相互依赖的定量关系的一种统计分析方法，运用十分广泛。其表达形式为y = w'x+e，e为误差服从均值为0的正态分布。\n",
    "\n",
    "回归分析中，只包括一个自变量和一个因变量，且二者的关系可用一条直线近似表示，这种回归分析称为一元线性回归分析。如果回归分析中包括两个或两个以上的自变量，且因变量和自变量之间是线性关系，则称为多元线性回归分析。 摘自百度百科\n",
    "\n",
    "简单的说： 线性回归对于输入x与输出y有一个映射f，y=f(x),而f的形式为aX+b。其中a和b是两个可调的参数，我们训练的时候就是训练a，b这两个参数。\n",
    "\n",
    "下面我们来用PyTorch的代码来做一个详细的解释"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "af4645d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'2.0.1'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 引用\n",
    "# 注意，这里我们使用了一个新库叫 seaborn 如果报错找不到包的话请使用pip install seaborn 来进行安装\n",
    "import torch\n",
    "from torch.nn import Linear, Module, MSELoss\n",
    "from torch.optim import SGD\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "torch.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc5a849f",
   "metadata": {},
   "source": [
    "下面定义一个线性函数，这里使用$y=5x+7$，这里的5和7就是上面说到的参数a和b，我们先使用matplot可视化一下这个函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d44f6d88",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x29e7b4730>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,20,500) # 从0到20的等差数列 500个数\n",
    "y = 5*x + 7\n",
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6b8eaca5",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.random.rand(256)\n",
    "noise = np.random.randn(256) / 4\n",
    "y = x * 5 + 7 + noise\n",
    "df = pd.DataFrame()\n",
    "df['x'] = x\n",
    "df['y'] = y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "de678db7",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/homebrew/Caskroom/miniconda/base/envs/d2l/lib/python3.8/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight\n",
      "  self._figure.tight_layout(*args, **kwargs)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(x='x', y='y', data=df);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc1126f1",
   "metadata": {},
   "source": [
    "我们随机生成了一些点，下面将使用PyTorch建立一个线性的模型来对其进行拟合，这就是所说的训练的过程，由于只有一层线性模型，所以我们就直接使用了"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c78e235b",
   "metadata": {},
   "outputs": [],
   "source": [
    "model=Linear(1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5c683af",
   "metadata": {},
   "source": [
    "其中参数(1, 1)代表输入输出的特征(feature)数量都是1. Linear 模型的表达式是 $y=wx + b$\n",
    "，其中 \n",
    " $w$代表权重， \n",
    " $b$代表偏置\n",
    "\n",
    "损失函数我们使用均方损失函数：MSELoss，这个后面会详细介绍"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a073a14c",
   "metadata": {},
   "outputs": [],
   "source": [
    "criterion = MSELoss() # 均方误差损失函数"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99e98edf",
   "metadata": {},
   "source": [
    "优化器我们选择最常见的优化方法 SGD，就是每一次迭代计算 mini-batch 的梯度，然后对参数进行更新，学习率 0.01 ，优化器本章后面也会进行介绍"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "01ed60e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "optim = SGD(model.parameters(), lr = 0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d078dfb8",
   "metadata": {},
   "outputs": [],
   "source": [
    "epochs = 3000"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17af442b",
   "metadata": {},
   "source": [
    "准备训练数据: x_train, y_train 的形状是 (256, 1)， 代表 mini-batch 大小为256， feature 为1. astype('float32') 是为了下一步可以直接转换为 torch.float"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "870ce41b",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train = x.reshape(-1, 1).astype('float32')\n",
    "y_train = y.reshape(-1, 1).astype('float32')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6812836d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 0, loss 106.1361\n",
      "epoch 100, loss 0.8699\n",
      "epoch 200, loss 0.1996\n",
      "epoch 300, loss 0.1632\n",
      "epoch 400, loss 0.1381\n",
      "epoch 500, loss 0.1188\n",
      "epoch 600, loss 0.1040\n",
      "epoch 700, loss 0.0926\n",
      "epoch 800, loss 0.0838\n",
      "epoch 900, loss 0.0771\n",
      "epoch 1000, loss 0.0719\n",
      "epoch 1100, loss 0.0679\n",
      "epoch 1200, loss 0.0648\n",
      "epoch 1300, loss 0.0625\n",
      "epoch 1400, loss 0.0607\n",
      "epoch 1500, loss 0.0593\n",
      "epoch 1600, loss 0.0582\n",
      "epoch 1700, loss 0.0574\n",
      "epoch 1800, loss 0.0568\n",
      "epoch 1900, loss 0.0563\n",
      "epoch 2000, loss 0.0559\n",
      "epoch 2100, loss 0.0556\n",
      "epoch 2200, loss 0.0554\n",
      "epoch 2300, loss 0.0552\n",
      "epoch 2400, loss 0.0551\n",
      "epoch 2500, loss 0.0550\n",
      "epoch 2600, loss 0.0549\n",
      "epoch 2700, loss 0.0549\n",
      "epoch 2800, loss 0.0548\n",
      "epoch 2900, loss 0.0548\n"
     ]
    }
   ],
   "source": [
    "for i in range(epochs):\n",
    "    # 整理输入和输出的数据，这里输入和输出一定要是torch的Tensor类型\n",
    "    inputs = torch.from_numpy(x_train)\n",
    "    labels = torch.from_numpy(y_train)\n",
    "    #使用模型进行预测\n",
    "    outputs = model(inputs)\n",
    "    #梯度置0，否则会累加\n",
    "    optim.zero_grad()\n",
    "    # 计算损失\n",
    "    loss = criterion(outputs, labels)\n",
    "    # 反向传播\n",
    "    loss.backward()\n",
    "    # 使用优化器默认方法优化\n",
    "    optim.step()\n",
    "    if (i%100==0):\n",
    "        #每 100次打印一下损失函数，看看效果\n",
    "        print('epoch {}, loss {:1.4f}'.format(i,loss.data.item()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1452b43a",
   "metadata": {},
   "source": [
    "训练完成了，看一下训练的成果是多少。用 model.parameters() 提取模型参数。 \n",
    "$w,b$ \n",
    " 是我们所需要训练的模型参数 我们期望的数据 \n",
    "$w=5，b=7$\n",
    " 可以做一下对比"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2d199c8d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.959712982177734 7.01079797744751\n"
     ]
    }
   ],
   "source": [
    "[w, b] = model.parameters()\n",
    "print (w.item(),b.item())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "9ba0a270",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 再次可视化一下我们的模型，看看我们训练的数据\n",
    "predicted = model.forward(torch.from_numpy(x_train)).data.numpy()\n",
    "plt.plot(x_train, y_train, 'go', label = 'data', alpha = 0.3)\n",
    "plt.plot(x_train, predicted, label = 'predicted', alpha = 1)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e13ac5d9",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "d2l",
   "language": "python",
   "name": "d2l"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.17"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
